How do you find the inverse of #f(x) = x – 7# and is it a function?

1 Answer
Aug 7, 2016

The inverse function is #f^-1(x)=x+7#

Explanation:

To find the inverse function of #y=f(x)# you have to calculate #x# as function of #y# and check if the formulka you get describes a function i. e. it has only one possible value for any argument.

In this example our function is #y=x-7#.

#y=x-7#

#y-x=-7#

#-x=-y-7#

#x=y+7#

It is a function. For any number #x# there is only one number #7# greater than #x#, so there is only one value.

Now we can write the inverse function using standard notation (##x# for argument and #y# for value).

The inverse is #y=x+7#